백준11408 열혈강호5

작성일 | In

문제 링크

  • http://icpc.me/11408

사용 알고리즘

  • MCMF
  • Network Flow

시간복잡도

  • O(VEf)

풀이

이분매칭을 max flow를 이용해 구하는 것과 같이 모델링을 해주고 MCMF를 돌려주면 됩니다.
최대 매칭의 수는 경로를 찾아 flow를 흘리는 횟수를 카운팅하면 됩니다.

전체 코드

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
#include <bits/stdc++.h>
using namespace std;

struct MCMF{
	int n;
	int c[1010][1010] = {0}; //capacity
	int f[1010][1010] = {0}; //flow
	int d[1010][1010] = {0}; //dist
	vector<int> g[1010]; //graph
	int source, sink;

	MCMF(){
		init(n);
	}

	MCMF(int n, int s, int t){
		init(n);
		source = s, sink = t;
	}

	void init(int _n){
		n = _n+1;
		source = sink = -1;
		memset(c, 0, sizeof c);
		memset(d, 0, sizeof d);
		memset(f, 0, sizeof f);
	}

	void setSource(int s){
		source = s;
	}

	void setSink(int t){
		sink = t;
	}

	void addEdge(int s, int e, int cap, int dist){
		g[s].push_back(e); c[s][e] = cap; d[s][e] = dist;
		g[e].push_back(s); c[e][s] = 0; d[e][s] = -dist;
	}

	int mcmf(){
		int cnt = 0;
		int minCost = 0;
		int prv[1010], dist[1010];
		bool inque[1010] = {0};
		while(1){
			memset(prv, -1, sizeof prv); memset(dist, 0x3f, sizeof dist); memset(inque, 0, sizeof inque);
			queue<int> q;
			dist[source] = 0;
			inque[source] = 1;
			q.push(source);

			while(q.size()){
				int now = q.front(); q.pop(); inque[now] = 0;
				for(auto nxt : g[now]){
					if(c[now][nxt] - f[now][nxt] > 0 && dist[nxt] > dist[now] + d[now][nxt]){
						dist[nxt] = dist[now] + d[now][nxt];
						prv[nxt] = now;
						if(!inque[nxt]){
							q.push(nxt);
							inque[nxt] = 1;
						}
					}
				}
			}
			if(prv[sink] == -1) break;
			int flow = 1e9+7;
			for(int i=sink; i!=source; i=prv[i]){
				flow = min(flow, c[prv[i]][i] - f[prv[i]][i]);
			}
			for(int i=sink; i!=source; i=prv[i]){
				minCost += flow * d[prv[i]][i];
				f[prv[i]][i] += flow;
				f[i][prv[i]] -= flow;
			}
			cnt++;
		}
		cout << cnt << "\n";
		return minCost;
	}
};

int main(){
	ios_base::sync_with_stdio(0); cin.tie(0);
	int n, m; cin >> n >> m;
	MCMF flow(1002, 1001, 1002);

	//cout << "init\n";

	for(int i=1; i<=n; i++){
		flow.addEdge(1001, i, 1, 0);
	}
	for(int i=501; i<=500+m; i++){
		flow.addEdge(i, 1002, 1, 0);
	}

	for(int i=1; i<=n; i++){
		int cnt; cin >> cnt;
		for(int j=0; j<cnt; j++){
			int a, b; cin >> a >> b;
			flow.addEdge(i, 500+a, 1, b);
		}
	}

	cout << flow.mcmf();
}